Question

The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price of two products, A and B, over time. The price f(x), in dollars, of product A after x years is represented by the function below: f(x) = 0.69(1.03)x
Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)


Part B: The table below shows the price f(t), in dollars, of product B after t years:

t (number of years) 1 2 3 4
f(t) (price in dollars) 10,100 10,201 10,303.01 10,406.04


Which product recorded a greater percentage change in price over the previous year? Justify your answer. (5 points)

Answer 1

Answer:

(A) The price of product A is increasing by 3% per year.

(B) The product A recorded a greater percentage change in price over the previous year.

Step-by-step explanation:

(A)

The function representing the price, in dollars, of product A after x years is:

$f_{A}(x)=0.69\cdot(1.03)x$

The function $f_{A}(x)$ can be written as:

$f_{A}(x)=0.69\cdot(1+0.03)x$

The function $f_{A}(x)$ is similar to the exponential growth function, $y=a(1+r)x$.

Here r is the growth rate.

Thus, it can be said that the price of product A is increasing by 3% per year.

(B)

Consider the data of product B for the year 3 and 4.

The price of product B for year 3 and 4 are 10,303.01 and 10,406.04.

Compute the percent price change from year 3 to 4 as follows:

$\text{Percent price change}=\frac{10406.04-10303.01}{10303.01}\times 100$

                                $=0.00999\times 100\\=0.999\%\\\approx1\%$

The price of product B is increasing by 1% per year.

Thus, the product A recorded a greater percentage change in price over the previous year.